R K Mecolt Singh filed the plea against the hospital, where his daughter allegedly got urinary tract infection while being under neo-natal intensive care after she was taken there for a routine check up, six days after her birth.
According to the complaint, Wahengbam Reenaka Devi delivered her baby at the hospital on November 15 and was discharged on November 20.
The complaint further claimed that the infant was admitted to the same hospital on November 26 after the doctors identified high billurubin count during routine check up.
The infant was shifted to another hospital at Saket on the same night as the previous hospital was not equipped to handle the case, the complaint said, adding she died on December 5.
The parents alleged that the doctor's "negligence and total callousness" had resulted in the "cruel fate" of an otherwise healthy and normal baby.
Police said a board of doctors will be constituted to look into any medical negligence for filing an FIR in this case.